All HSPT Math Resources
Example Questions
Example Question #1 : Find Areas Of Rectilinear Figures: Ccss.Math.Content.3.Md.C.7d
What is the area of the figure below?
To find the area of the figure above, we need to split the figure into two rectangles.
Using our area formula, , we can solve for the area of both of our rectangles
To find our final answer, we need to add the areas together.
Example Question #237 : Geometric Measurement: Understanding Concepts Of Area And Relating Area To Multiplication And To Addition
If the formula to find the area of the white section of the rectangle below is , what is the formula to find that area of the purple section?
Both the purple section and the white section have the same length, . The width of the purple section is . Thus the area formula for the purple section of the rectangle is .
Example Question #111 : Geometry
What is the perimeter of a figure with seven sides, four of which measure 9 inches, two of which measure 10 inches, and one of which measures a foot?
Add the side measures, in inches (changing one foot to 12 inches):
Example Question #112 : Geometry
What is the perimeter of a right triangle with hypotenuse and a leg of length ?
It cannot be determined from the information given.
Using the Pythagorean Theorem, the length of the second leg can be determined.
We are given the length of the hypotenuse and one leg.
The perimeter of the triangle is the sum of the lengths of the sides.
Example Question #2 : How To Find The Perimeter Of A Right Triangle
Which of these polygons has the same perimeter as a right triangle with legs 6 feet and 8 feet?
None of the other responses is correct.
A regular decagon with sidelength one yard.
A regular octagon with sidelength one yard.
A regular pentagon with sidelength one yard.
A regular hexagon with sidelength one yard.
A regular octagon with sidelength one yard.
A right triangle with legs 6 feet and 8 feet has hypotentuse 10 feet, as this is a right triangle that confirms to the well-known Pythagorean triple 6-8-10. The perimeter is therefore feet, or 8 yards.
We are looking for a polygon with this perimeter. Each choice is a polygon with all sides one yard long, so we want the polygon with eight sides - the regular octagon is the correct choice.
Example Question #262 : Plane Geometry
The perimeter of the following trapezoid is equal to 23 cm. Solve for . (Figure not drawn to scale.)
The perimeter is equal to the sum of all of the sides.
Example Question #1 : How To Find The Perimeter Of Square
Use this image for the following problem.
What is the perimeter of the square in this picture?
The question only is looking for a part of the picture, just the square. With squares, the rule is that all the sides are equivalent, meaning the same lengths and all angles are right angles.
Perimeter means adding up all the sides together. So we just need to add the lengths of the sides of the square. Uh oh, we only have one side that is listed.
Again, remember that with squares the sides are equivalent, and we know one side is 5 inches. We just need to take because a square has 4 sides.
Our perimeter is .
Example Question #1 : Quadrilaterals
Sandy wants to put a border around her son’s nursery. If all four square walls in the room have the same width and use up feet of border, what is the length of one wall?
When Sandy puts the border around her son's room, she will need enough to cover the perimeter. Since the room has four walls equal in length, we know that the room is a square. The perimeter of a square can by found by adding all the sides together, or by multiplying the length of one side by 4. This can be written as:
Since we know that Sandy used feet of border, we know the perimeter is . We can now write an equation:
Now, in order to isolate the variable, we can divide both sides by four.
The left-hand side simplifies to:
The right-hand side simplifies to:
When we solve, we find that the length of each wall is .
Example Question #2 : Quadrilaterals
Find the perimenter:
The perimeter is equal to the sum of the length of all sides. Each side is equal to . Therefore, the perimeter equals:
Example Question #115 : Geometry
You are given equilateral triangle and Rectangle
with .
What is the perimeter of Rectangle ?
is equilateral, so .
Also, since opposite sides of a rectangle are congruent,
and
The perimeter of Rectangle is